Spectroscopy uses the interaction of a radiation with a material sample to perform a spectral characterization. Fourier Transform Spectroscopy is an analysis method long used for its spectral accuracy and energy efficiency in environmental monitoring and in forensic analysis among many applications. Frequency comb spectroscopy uses electromagnetic pulses which provide a wide frequency range for the analysis. Frequency comb spectroscopy generally requires a pulsed light source generating the frequency comb.
In U.S. Pat. No. 5,748,309, a Fourier Transform Spectroscopy (FTS) method combining two frequency combs is proposed. The proposed method combines in the optical domain two frequency combs, namely mode-locked lasers, having slightly detuned repetition rates fr, and measures the beating spectra in the Radio Frequency (RF) domain, i.e. the RF beating replica of the optical domain spectrum to be characterized. The beating spectra are obtained by performing a Fourier transformation of the measured time response of the source interference signal (interferogram) in the considered RF band. The stability of the source combs is vital to ensure that the RF beating replica is consistent during a whole measurement interval. Even minor variations of fr and of the carrier envelope offset (CEO) f0 of any of the mode-locked lasers changes the mapping between the RF beating replica and the optical domain spectrum, thus severely limiting the accuracy of the Fourier transform of the interferogram. In order to maintain the mapping constant between the RF beating replica and the optical domain spectrum, the constraints are extremely high on the stability of the repetition rates and of the carrier envelope offset frequencies of both mode-locked lasers.
I. Coddington, W. C. Newbury and N. R. Newbury, “Coherent multiheterodyne spectroscopy using stabilized optical frequency combs”, Physical Review Letters 100, 013902 (2008) reports high-resolution complex spectroscopy using mode locked fiber lasers stabilized on two narrow continuous wave fiber lasers. This method transfers the continuous wave laser stability, on the frequency comb beating frequency, but is also sensitive to any remaining instabilities of the continuous wave laser.
The frequency of any line of a mode-locked laser is fully described by the laser repetition rate fr and the carrier envelope offset frequency f0. The optical referencing is achieved for stabilized values of fr and f0. In D. J. Jones, S. A. Diddams, J. K. Randa, A. Stentz, R. S. Windeler, J. L. Hall and S. T. Cundiff, “Carrier-Envelope Phase Control of Femtosecond Mode-Locked Lasers and Direct Optical Frequency Synthesis”, Science Vol. 288, pp. 635-639 (2000), an auto-referencing of mode-locked frequency comb is proposed using the so-called 1f-2f technique for sources with a spectrum spanning of at least an octave. Using the 1f-2f technique, the carrier envelope offset frequency is canceled and in the case where the repetition rate is also actively locked, long-term stability and referencing of the optical comb is achieved with state of the art accuracy. Some limitations of the 1f-2f techniques are the short-term instabilities induced or left by the active feedback of the mode-locked lasers, and the overall complexity of construction.
Regarding the dual comb Fourier transform technique, international patent application bearing publication no. WO 2007/045461 A1 provides a way to improve the measurement duty cycle by periodically changing the repetition rate of one of the lasers in order to scan only the desired portion of the cross-correlation function, while still relying on the stability of the sources for the measurement duration. U.S. patent application bearing publication no. 2007/0182966 A1 provides an apparatus and method to conduct frequency comb heterodyne spectroscopy with continuous wave lasers. With this method, more than two parameters are likely to be needed to define the mapping between the RF beating replica and the optical domain spectrum.
Therefore, there is a need to address the stability issues of sources such as frequency comb sources when analyzing samples.